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Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models

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  • Yufeng Wang
  • Youhua Qian
  • Bingwen Lin

Abstract

In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.

Suggested Citation

  • Yufeng Wang & Youhua Qian & Bingwen Lin, 2020. "Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models," Complexity, Hindawi, vol. 2020, pages 1-11, September.
    • Handle: RePEc:hin:complx:1351397
    DOI: 10.1155/2020/1351397
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    Cited by:

    1. Youhua Qian & Yuhui Peng & Yufeng Wang & Bingwen Lin, 2022. "Relaxation Oscillations and Dynamical Properties in a Time Delay Slow–Fast Predator–Prey Model with a Piecewise Smooth Functional Response," Mathematics, MDPI, vol. 10(9), pages 1-11, April.

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